Cyclotrons and particle ionisation

If a cyclotron is being used to accelerate particles, it is obviously ideal to have bare nuclei as this will substantially increase the rotational frequency, and thus the velocity and particle energies.

It can be shown from the formula [itex]f=\frac{B q}{2 \pi m}[/itex] that the frequency increases linearly with charge (ignoring the mass of the electrons). For example, if various ions of boron are being accelerated in a certain cyclotron, and B+ has a frequency of 2 MHz, then B2+ will have f of 4 MHz, and bare boron, B5+, will have f of 10 MHz. In this case, could a 10 MHz RF field be used for all these ions at the same time, as long as the dees are sufficiently close that less ionised particles won't be affected by the electric field switching whilst they are outside of the dees?

Also, will the ions become more ionised as they are accelerated, so that all the particles are eventually stripeed of all their electrons? If so, could the free electrons be removed by grounding the dees?

Lastly, roughly how efficient could you make this cyclotron in converting input power into kinetic energy, using a permanent magnet to reduce the energy requirements? Would an electromagnet severely reduce the efficiency, even though it isn't actually transferring energy to the particles?

Frequency is not important. Technically, you may equally easy create frequencies od kHz or GHz.
The difference is in the size of cyclotron (radius of particle orbit). Usually it is easier and cheaper to build smaller device - thus accelerate pure nuclei rather than ions 1+.
But, on the other hand, particles (ions, nuclei...) circulating with small radius, emits more synchrotron radiation (losing energy) than those running over wider orbits. So if you want to achieve higher energies - you should build bigger device and populate it with B+.

No, ions don't lose their electrons, as they are accelerated.

Permanent magnet: excercise for you: google for strongest permanent magnet ever built, and compare it with magnetic field required by cyclotron... It is not electromagnet which transfers energy to particles. Actually, the energy powering the electromagnets is just wasted. All energy transfereed to particles comes from RF.

Thanks very much for answering all those questions :) The reason for them is that I'm thinking of building an experimental device, which needs low energy accelerators and bare nuclei, and I though one or two small cyclotrons might be able to accomplish both of those. I only need a few hundred keV, and N45/48 neodymium magnets with 1.38 Tesla will be perfectly fine for a 5cm radius cyclotron, and bremsstrahlung/synchrotron radiation shouldn't be a big problem at these energies.

Obviously the magnetic flux will be less than the amount quoted at the centre of the chamber, but when I get that far in the design I should be able to work around that with a more powerful magnet (commercial neodymium magnets go up to 1.48 Tesla), by bringing them closer together or simply increasing the radius. Just out of interest, do you know how much the flux decreases by if particles are in the middle of a 1cm gap between the two magnets? And how far does the flux at this magnitude extend out of the magnet, so I don't need to buy 10cm diameter magnets ?

I hope I'm right in thinking I only need a vacuum chamber, two hollow conductive copper plates, two static magnets, a high voltage RF oscillator and a high-vacuum pump to create a cyclotron, right? :)

Back to the original question :rofl:, if I can't use a cyclotron to complete the ionisation, how else should I go about it? Would heating the ions in the chamber work or are there more efficient ways? Could I get a large amount of bare boron nuclei by colliding them with an electron beam, or should I force B+ through thin foil? I can't seem to find out what's the cheapest, fastest and most energy efficient way to get these specific bare nuclei? The 5+ ionisation energy is about 13000 kJ/mol, but anything below 100,000 kJ/mol is acceptable energy usage for me.

You may want to look at some web pages of peaople, who built amateur cyclotrons. There are lots of technical issues you must solve (shaping the magnetic flux, shaping EM-field, etc)

Your beam does not affect magnetic flux at all.

You need also a source of ions, and a mechanism (window, beam pipe) transporting accelerated ions towards your target.

As for my intuition (disclaimer - I havent ever worked with ions in 1 MeV range) if you send them through thin metal foil all electrons should get stripped.

anything below 100,000 kJ/mol is acceptable energy usage for me.

I am afraid your expectations are unrealistic by many orders of magnitude. I doubt if you may achieve the beam current of more than 1 microamper => ion flux of 10-11mol/s. It would mean your machine should operate with power consumption of 1 mW. Actually, I doubt if amateur cyclotron may reach even 1 microamper.

Hmm... OK well I think I have enough information now to get the particles ionised now, but as for the actual cyclotron, looking at web pages, I don't see a lot of discussion on technical issues. I'm aware that the particles may drift up or down, parallel to the magnetic field, which I assume can be corrected with positive voltage plates on the top and bottom of the chamber? The only major issue I can see right now is if the guiding centre has the potential to move a lot...

Is the guiding centre a property of the magnets, so that it should always be relatively close to the central axis of the magnets, or is it independent of the magnetic field, and free to drift wherever the particle goes? In my cyclotron, the particles would probably be deflected by other charges fairly often, so I'd hope that they would continue orbiting the same axis, and thus the magnetic and EM fields would eventually stabilise the orbits, but if the guiding centre is independent of the magnets I'll need to considerably rethink my design...